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Simplifying 17x2 + 32x + -660 = 0 Reorder the terms: -660 + 32x + 17x2 = 0 Solving -660 + 32x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -38.82352941 + 1.882352941x + x2 = 0 Move the constant term to the right: Add '38.82352941' to each side of the equation. -38.82352941 + 1.882352941x + 38.82352941 + x2 = 0 + 38.82352941 Reorder the terms: -38.82352941 + 38.82352941 + 1.882352941x + x2 = 0 + 38.82352941 Combine like terms: -38.82352941 + 38.82352941 = 0.00000000 0.00000000 + 1.882352941x + x2 = 0 + 38.82352941 1.882352941x + x2 = 0 + 38.82352941 Combine like terms: 0 + 38.82352941 = 38.82352941 1.882352941x + x2 = 38.82352941 The x term is 1.882352941x. Take half its coefficient (0.9411764705). Square it (0.8858131486) and add it to both sides. Add '0.8858131486' to each side of the equation. 1.882352941x + 0.8858131486 + x2 = 38.82352941 + 0.8858131486 Reorder the terms: 0.8858131486 + 1.882352941x + x2 = 38.82352941 + 0.8858131486 Combine like terms: 38.82352941 + 0.8858131486 = 39.7093425586 0.8858131486 + 1.882352941x + x2 = 39.7093425586 Factor a perfect square on the left side: (x + 0.9411764705)(x + 0.9411764705) = 39.7093425586 Calculate the square root of the right side: 6.301534937 Break this problem into two subproblems by setting (x + 0.9411764705) equal to 6.301534937 and -6.301534937.Subproblem 1
x + 0.9411764705 = 6.301534937 Simplifying x + 0.9411764705 = 6.301534937 Reorder the terms: 0.9411764705 + x = 6.301534937 Solving 0.9411764705 + x = 6.301534937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9411764705' to each side of the equation. 0.9411764705 + -0.9411764705 + x = 6.301534937 + -0.9411764705 Combine like terms: 0.9411764705 + -0.9411764705 = 0.0000000000 0.0000000000 + x = 6.301534937 + -0.9411764705 x = 6.301534937 + -0.9411764705 Combine like terms: 6.301534937 + -0.9411764705 = 5.3603584665 x = 5.3603584665 Simplifying x = 5.3603584665Subproblem 2
x + 0.9411764705 = -6.301534937 Simplifying x + 0.9411764705 = -6.301534937 Reorder the terms: 0.9411764705 + x = -6.301534937 Solving 0.9411764705 + x = -6.301534937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9411764705' to each side of the equation. 0.9411764705 + -0.9411764705 + x = -6.301534937 + -0.9411764705 Combine like terms: 0.9411764705 + -0.9411764705 = 0.0000000000 0.0000000000 + x = -6.301534937 + -0.9411764705 x = -6.301534937 + -0.9411764705 Combine like terms: -6.301534937 + -0.9411764705 = -7.2427114075 x = -7.2427114075 Simplifying x = -7.2427114075Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.3603584665, -7.2427114075}
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